The present invention relates generally to the field of relatively high temperature measurement of heated gaseous plasmas in a medium which is not strictly controllable.
The best methods of existing plasma-temperature measurements make use of spectrographic techniques. Confining the range of temperatures discussed to less than of the order of 50,000.degree.K, the principles of so-called "spectroscopic thermometry" in this range have been discussed, for example, by National Bureau of Science (NBS) research workers (N.B.S Special Publication 333, Vol. 2 pp. 407-443, August 1968) and also by W. Lochte-Holtgreven (Reports of Progress in Physics, Vol. XXI, pp. 312-383 (1958)).
As described by Lochte-Holtgreven, the spectrographic temperature-measurement method requires the solution of a number of equations involving certain unknowns such as: temperature T, and densities of a number of species of atoms and ions in the plasma. For example, in a 3-component plasma composed of air (i.e. nitrogen and oxygen) and hydrogen. For this plasma, in the temperature range of interest there are 8 unknowns which include: temperature T, electron density n.sub.e, and n.sub.+ and n.sub.o the positive ion and neutral atom densities of each species. An accurate evaluation of T, therefore, requires establishing 8 equations, 6 of which are as follows: EQU (n.sub.N.sub.+) + (n.sub.N) + (n.sub.O.sub.+) + (n.sub.O) + (n.sub.H.sub.+) + (n.sub.H) = (N) (1). EQU (n.sub.N.sub.+) + (n.sub.N) = 3.72 [ (n.sub.O.sub.+) + (n.sub.O)](2). EQU (n.sub.N.sub.+) + (n.sub.O.sub.+) + (n.sub.H.sub.+) = (n.sub.e) (3). EQU (n.sub.+ ) .sup.. (n.sub.e)/(n) = f(T) for H, N and O (4)
where (N) is the total number-density of particles in the plasma, (n.sub.+) and (n) denote densities of positive ions and neutral atoms, respectively, of each of the 3 species, and f(T) is the function of T which appears in the Saha equation, i.e. considering only singly ionized species: ##EQU1## WHERE K AND H ARE Boltzmann's and Planck's constants, respectively, E is the ionization energy of each particular species (i.e. H, N or O) and m is the electronic mass. Two further equations are still needed for a complete solution. These equations must be obtained from some experimental determinations of the physical condition of the plasma.
Usually the method has been to determine the necessary equations from measurements of spectral-line intensities. The intensity I.sub.m,r of a line emitted in a transition between levels m and r of a species (which may be neutral or ionized) in local thermodynamic equilibrium (LTE) with the plasma is given by: EQU I.sub.m,r = A.sub.r,m .sup.. g.sub.m /U n.h.nu. .sup.. exp (-E.sub.m/ kT.sub.e) (8).
where A.sub.r,m is the Einstein transition probability between the states r and m, g.sub.m is the statistical weight of state m, U is the partition function for the neutral or positive ion species of number density n, and E.sub.m is the excitation energy of the state m above the ground level.
Since it is generally considered that a plasma, being in a static or semi-static condition, is in the local thermodynamic equilibrium (LTE), the electron temperature T.sub.e is assumed to be equal to the gas temperature T of the plasma. Furthermore, if the sample of plasma from which the line is observed is optically thin, it may be considered, for all practical purposes, that the measured line intensity is identical with the theoretical value given in Eq (8). In principle, therefore, measurement of the intensities of two lines from any species of the plasma then completes the number of equations required and allows a temperature to be evaluated.
Certain alternative spectrographic measurements may be considered in place of either or both of the last two equations just mentioned. As Lochte-Holtgreven pointed out, one alternative is to measure n.sub.e, the electron density, instead of one of the line intensities. The electron density in a plasma can be measured by determining the shape of certain lines broadened by the surrounding ionized plasma. Theory of the Stark Effect can then be employed to relate the line shape to the electron density and plasma temperature.
In the case of a lightning-column plasma (as well as other cases of externally uncontrolled plasmas) it is not possible to specify at any particular time the total density, N, of particles in the plasma. This means that Eq (1) cannot be established and consequently n in Eq (8) is unspecifiable. The technique just described is therefore inoperable. In this case it has been the practice in lightning-temperature measurements, following Prueitt and Orville (Jour. Geophys. Res. 68, p. 803 (1963), and Journ. Atmos. Sci. 25, p. 827, 839 (1968)) to eliminate n from Eq (8) by determining the ratios of intensities of pairs of spectral lines emitted from the same species. Thus, for two lines of frequencies .nu. .sub.m,r and .nu..sub.p,q, the ratio of intensities I.sub.m,r and I.sub.p,q is given by: ##EQU2##
Since parameters: A, g, .nu. and E are known either from theory or from basic spectroscopic data, the value of T can be obtained from an experimental measurement of the ratio I.sub.m,r /I.sub.p,q and use of Eq (9).
The basic assumptions of the foregoing spectrographic methods are: (1) that local thermodynamic equilibrium holds in the plasma region and (2) that the plasma responsible for the observed emission is optically thin.
Under normal circumstances of spectrographic observations (where the duration times of observation are longer than of the order of microseconds which are the normal times of equilibration) it is very probable that the assumption of LTE is valid. However, with respect to the second assumption cited above, and certainly under conditions external to the laboratory (and even under some laboratory conditions) it is improbable that emissions occur from a volume region of the plasma which is optically thin. An analysis of emission line radiation from a typical lightning channel by Hill (Journ. Geophys. Res. 77, p. 2642 (1972)) showed that most radiations are moderately strongly absorbed in emerging from the channel. Thus in reality a plasma cannot be treated as optically thin.